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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

An example on the Mann iteration method for Lipschitz pseudocontractions


Authors: C. E. Chidume and S. A. Mutangadura
Journal: Proc. Amer. Math. Soc. 129 (2001), 2359-2363
MSC (2000): Primary 47H09, 47J25
Published electronically: January 18, 2001
MathSciNet review: 1823919
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Abstract:

An example of a Lipschitz pseudocontractive map with a unique fixed point is constructed for which the Mann iteration sequence fails to converge. This resolves a long standing open problem.


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Additional Information

C. E. Chidume
Affiliation: The Abdus Salam International Centre for Theoretical Physics, 34100 Trieste, Italy
Email: chidume@ictp.trieste.it

S. A. Mutangadura
Affiliation: Department of Physics, University of Zimbabwe, Harare, Zimbabwe

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06009-9
PII: S 0002-9939(01)06009-9
Received by editor(s): December 14, 1999
Published electronically: January 18, 2001
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2001 American Mathematical Society